**4. Fuzzy Logic-Based Controller**

A dynamic droop controller based on fuzzy logic is designed to support the grid's frequency of WES. The fuzzy logic controller is a set of rules are defined to perform a certain function [45]. The concept of fuzzy logic has been used in control applications of the electrical grid and power electronics [46–50].

Fuzzy logic is implemented to determine the slope of the droop curve depending on the available reserved power of WES and the ROCOF. For instance, when the change of frequency is high, and the power reserve is not large, the WES must support the frequency by providing active power with a slow rate. In the other hand, when the power reserve is high, WES should support the frequency by rapidly providing the required active power.

The equation that relates the grid's frequency and active power are:

$$P\_{PFC} = \frac{P\_{\text{WT,arcu}}}{R\_t} \frac{(f\_{\text{nom.}} - f\_{\text{grid}})}{f\_{\text{nom.}}} \tag{3}$$

This fuzzy logic-based controller aims to give an appropriate dynamic rate ( *Rt*). The output of the fuzzy logic controller depends on two inputs. The inputs are the ROCOF, and the power reserved by the WES (Δ*PWT*) at the time of frequency drop. The reserved power of WES varies according to the wind velocity and the de-loading method used by the central controller of a wind plant. Also, the wake-effect plays a vital role on the power availability for each individual WES. Therefore, each WES has a different power reserve to others.

Figure 2 demonstrates the implementation of fuzzy-logic with the dynamic droop controller. Normally, the wind speed, *VW*, can be measured to estimate the maximum power of the turbine, *PWT*, *max*. The maximum power is decreased by Δ*PWT* to maintain a certain reserve. Every individual WES is de-loaded to maintain a certain reserve of power (Δ*PWT*) to be utilized to provide APC during a drop in the grid's frequency. When grid's frequency drops below its set point, the controller injects a certain amount of active power into the grid. Then, this power, PFC, is added to the loop to produced power to form a reference of the required total wind power. The reference point, *PWT*, of the total power is then achieved either by using a pitch angle or rotor speed controller.

**Figure 2.** The implementation of fuzzy logic within the active power controller.
